{
  "id": "2308.08338",
  "version": "v1",
  "published": "2023-08-16T12:57:11.000Z",
  "updated": "2023-08-16T12:57:11.000Z",
  "title": "On the exactness of the conditions of embedding theorems for spaces of functions with mixed logarithmic smoothness",
  "authors": [
    "Gabdolla Akishev"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2308.06737",
  "categories": [
    "math.CA"
  ],
  "abstract": "The article considers the Lorentz space $L_{p,\\tau}(\\mathbb{T}^{m})$, $2\\pi$ of periodic functions of many variables and $S_{p,\\tau,\\theta}^{0, \\overline{b}}\\mathbf{B}$, $S_{p, \\tau, \\theta}^{0, \\overline{b}}B$ -- spaces of functions with mixed logarithmic smoothness. The article establishes necessary and sufficient conditions for embedding the spaces $S_{p, \\tau, \\theta}^{0, \\overline{b}}\\mathbf{B}$ and $S_{p, \\tau, \\theta}^{ 0, \\overline{b}}B$ into each other.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-16T12:57:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "41A10",
      "41A25",
      "42A05"
    ],
    "keywords": [
      "mixed logarithmic smoothness",
      "embedding theorems",
      "article establishes necessary",
      "lorentz space",
      "periodic functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}